確率９：n数の和と倍数の確率《一橋大2013年》

Homepage: http://mathematics-monster.jp All course problems can be viewed and printed from the homepage. I apologize if the writing on the blackboard in this lesson is difficult to read due to its small size. I recommend taking the course on a tablet or computer. I'm mentally exhausted from continuing to film, so I might suspend filming until September. I might be able to film up to probability lesson 10 before summer, but every year it's too hot to film in the summer. The air conditioning picks up noise with the microphone, and I have five lights in front of the blackboard, so by June it's already too hot and sweaty to film. More than anything, I've been filming continuously since September of last year, and I'm reaching my mental limit. For those of you currently watching who will be taking the exam next year, please take lessons 10 onwards from the previous probability lessons. In any case, I think I'll only be able to re-record up to probability lesson 20 before next year's exam. Unlike last year's test-takers, I've finished filming all the vector lessons, so please bear with me. I'm going to diligently work on reviewing probability problems, even if it means crawling on my hands and knees, for the sake of students taking exams five or ten years from now. At the end of March, I went to Niigata with my family and met up with two friends I hadn't seen in over ten years, on separate days. Both friends are married, so I also met their families. With both friends, we only managed to meet for a few hours, including each other's families, so we couldn't really talk about our student days at length. I felt that we'll have to put off reminiscing until our children are older and we can visit each other without having to leave them behind. In the past few months, I've tried contacting more than 15 friends from my student days, all of whom I hadn't seen in over ten years, but half of them haven't replied. I think that as we get older, everyone's life stages are so different that even if we met, the conversation wouldn't really connect, which is probably why they don't feel like replying. There are all sorts of people who don't reply: single people who are fully dedicated to their work, people who are exhausted from work and barely able to survive, people who want to get married but aren't succeeding, people whose marriages aren't going well, working parents raising children and whose days are like a battlefield, divorced people, and so on. There are all sorts of life stages, and some people simply don't want to be in contact with someone like Sugitani anymore. I think everyone probably has their own reasons for not replying. Most of the people who reply are those whose lives are going smoothly. They're either happily married or happily raising children; basically, it's one or the other. Among those who replied, there's a friend I met while working part-time as a tutor during university. He was a friend who studied at home before getting into the science department at the University of Tokyo, and back then, he often solved the math problems I created. I remember him saying, "You're a genius!" when I revealed the secret behind a riddle-like probability recurrence relation I had created. I also remember going to Gusto (a restaurant chain) with him and playing Pokémon battles on his DS. I rarely lose to people I know, but I remember losing to him. Incidentally, we're the same age. The last time I was in contact with this friend was in 2015, so it's been 11 years since we last spoke. Back then, he told me he was busy preparing for his wedding. In this recent message, he informed me that his wife had passed away from cancer two years ago. Since receiving that message, it's been weighing heavily on my mind. He said he's currently raising two elementary school-aged children while working, and that perhaps we won't be able to meet for tea until 10 years from now, when things have settled down. I replied, "I'll definitely contact you in 10 years! Let's have tea then." As anyone who regularly reads my posts here will know, I live my life as if I could die at any time. Choosing my words carefully is incredibly difficult, as I don't want to offend a close friend, but this has given me a renewed sense of gratitude for having lived this long. I feel it's a miracle that I'm still in this world, that I can live my life the way I want, and that I'm able to continue filming my lessons little by little this year. And over and over again, I imagined myself leaving this world today or tomorrow, and my wife and children leaving this world today or tomorrow. I am happy that I can leave this writing in this world.